# All-electron machine-learned orbital-free density functional for periodic CHNO systems

arXiv: https://arxiv.org/abs/2610.17975 · HTML: https://mlsanity.com/paper/2610.17975/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 69 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 9 of 9)

- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passing](https://mlsanity.com/paper/2405.15389/) (2024)
- [Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning](https://mlsanity.com/paper/2309.16578/) (2023)
- [Variational principle to regularize machine-learned density functionals: the non-interacting kinetic-energy functional](https://mlsanity.com/paper/2306.17587/) (2023)
- [Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory](https://mlsanity.com/paper/2502.05411/) (2025)
- [Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blink](https://mlsanity.com/paper/2601.19966/) (2026)
- [Surrogate Functionals for Machine-Learned Orbital-Free Density Functional Theory](https://mlsanity.com/paper/2604.20458/) (2026)
- [Orbital-Free Density Functional Theory Implementation with the Projector Augmented-Wave Method](https://mlsanity.com/paper/1408.4701/) (2014)
- [DeePAW: A universal machine learning model for orbital-free ab initio calculations](https://mlsanity.com/paper/2603.18650/) (2026)

## Abstract (arXiv)

We introduce STRUCTURES-P, a machine-learned all-electron orbital-free density functional for periodic CHNO systems. Electrostatics are evaluated analytically in an atom-centered Gaussian basis, while an equivariant network learns the kinetic and exchange-correlation energy from energies and gradients of non-ground-state densities. Minimizing the functional from a superposition of atomic densities recovers the Kohn-Sham ground state: on held-out crystals, the density error falls from 6.7% to 0.4% of the electron count and the energy error reaches 0.25 mHa per atom, half that of a same-architecture interatomic potential. A single functional can be trained for both isolated molecules and periodic systems, and the model generalizes to larger unit cells. It largely preserves relative-energy rankings and reproduces convex-hull vertices on the tested H-N composition slice. Together, these results demonstrate the viability of machine-learned all-electron orbital-free DFT for variational density optimization and energy evaluation in fixed-geometry solids.